# Volume of Cube changing with respect to time.

• A_Munk3y
In summary, volume is the amount of space occupied by a three-dimensional object. The volume of a cube is calculated by multiplying its length, width, and height. The volume of a cube can change over time due to changes in its dimensions, temperature or pressure, chemical reactions, and physical processes. To measure the change in volume of a cube over time, various methods such as displacement, water displacement, or using instruments like a graduated cylinder or a balance can be used to track the difference in volume at different points in time.
A_Munk3y

## Homework Statement

The volume V of a cube with sides of length x in. is changing with respect to time. At a certain instant of time, the sides of the cube are 5 in. long and increasing at the rate of 0.1 in./sec. How fast is the volume of the cube changing at that instant of time?

## The Attempt at a Solution

dv/dt = dx/dt*3x2
dx/dt=0.1 x=5
dv/dt=0.1(3*52)=7.5 cu in/sec

am i correct in my answer?

Looks right.

thanks! :)

## What is the definition of volume?

Volume is the amount of space occupied by a three-dimensional object.

## How is the volume of a cube calculated?

The volume of a cube is calculated by multiplying the length, width, and height of the cube. The formula for volume is V = lwh, where V is volume, l is length, w is width, and h is height.

## Can the volume of a cube change over time?

Yes, the volume of a cube can change over time if any of its dimensions (length, width, or height) change. For example, if the cube is melting or evaporating, its volume will decrease over time.

## What factors can cause the volume of a cube to change?

The volume of a cube can change due to changes in its dimensions, changes in temperature or pressure, chemical reactions, and physical processes such as melting, dissolving, or evaporating.

## How can we measure the change in volume of a cube over time?

The change in volume of a cube over time can be measured using various methods such as displacement, water displacement, or by using instruments like a graduated cylinder or a balance. These methods allow us to calculate the difference in volume at different points in time and track the change over time.

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